Hello everyone, today we're going to discuss the ancient measurement systems. The "Zhou Li" mentions a measuring vessel called "hu," which is one foot deep, has an inner square of one foot, and an outer circle, with a total volume of one "hu"; its base is one inch, with a volume of one "dou"; its handles are three inches, with a volume of one "sheng." The total weight is one "jun," and it produces a sound that matches the pitch of the yellow bell, exempt from taxation. It is inscribed with a saying: "Through reflection and thought, we have achieved excellence. With the fine measurements established, let the four nations observe. For generations to come, this vessel shall serve as a standard." This means that after repeated contemplation, a finely crafted measuring vessel was ultimately created for the nations of the world to reference, benefiting future generations and becoming a standard.
The "Zuo Zhuan" also mentions four types of measuring vessels used in the state of Qi: "dou," "qu," "hu," and "zhong." Four "sheng" make one "dou," and similarly, four "dou" make one "hu," which equals six "dou" and four "sheng" in total; ten "hu" make one "zhong," equating to sixty-four "dou." Zheng Xuan believed that the area of a square foot equals one thousand inches, which differs from the result in the "Nine Chapters on the Mathematical Art" by two "sheng," eighty-one "fen," and two "zhi." Zu Chongzhi used a more precise calculation method and determined its volume to be one thousand five hundred sixty-two and a half inches. If we consider the shape of a square foot comprising an inner square and outer circle, the diameter is approximately one foot, four inches, one-tenth, four milliseconds, and two microseconds, and the depth is one foot, which is the standard for the ancient "hu."
The "Nine Chapters on Commercial Calculation" records that the volume of one "hu" of grain is two thousand seven hundred inches, one "hu" of rice is one thousand six hundred twenty inches, and one "hu" of beans, hemp, and wheat is two thousand four hundred thirty inches. This shows that ancient people established different measurement standards based on the varying densities of grains to ensure equitable pricing. Using the rice "hu" as a standard is similar to what is recorded in the "Book of Han." The "Sunzi Suanshu" states: six grains of millet make one "gui," ten "gui" make one "miao," ten "miao" make one "cuo," ten "cuo" make one "shao," and ten "shao" make one "he." Ying Shao explained that "gui" is a natural shape, the origin of yin and yang, with four "gui" making one "cuo"; Meng Kang said that sixty-four grains of millet make one "gui."
The "Book of Han" states that the measuring vessels are the yue, he, sheng, dou, and hu, used to measure quantity. Initially, the yue was crafted based on the pitch of the Huangzhong, with standard measuring instruments to measure volume, filled with selected grains (jiu shu) and calibrated for levelness using well water. One he equals one yue, ten he equals one sheng, ten sheng equals one dou, and ten dou equals one hu, thus completing these five measuring vessels. The manufacturing method involves making a square measure from copper, with a round exterior and a raised portion on the side. The top is hu, the bottom is dou, the left side is sheng, and the right side has both he and yue. Its shape resembles a jue, symbolizing nobility. Three above and two below symbolize heaven and earth; round and inner square, with one on the left and two on the right, symbolize yin and yang. The circular shape symbolizes a compass, weighing two jun, containing quantities of various gases and substances, each amounting to eleven thousand five hundred twenty. The sound is consistent with the Huangzhong, starting from the Huangzhong and repeating. The inscription on the hu reads: "The law of the good measure hu, square measure and round outside, with a side raised nine li and five mao, a depth of one foot, accumulating one thousand six hundred twenty inches, holding ten dou." Zu Chongzhi calculated using pi, stating that the diameter of this hu is approximately one foot, four inches, three tenths, six hundredths, one millimeter, and two tenths of a millimeter, with the raised portion about one tenth and nine mao in height. Liu Xin calculated the raised portion to be one li and four mao less, due to inaccuracies in his calculation method. In 227 AD, Liu Hui, while annotating the "Nine Chapters on the Mathematical Art," stated: "The hu used by the current Grand Minister of Agriculture has a diameter of one foot, three inches, five tenths, and five hundredths, and a height of one foot, with a volume of one thousand four hundred forty-one and three-tenths inches. The copper hu from Wang Mang's period, when calculated with today's measurements, has a height of nine inches, five tenths, and five hundredths, with a diameter of one foot, three inches, six tenths, eight hundredths, and seven mao. Using my calculation method, the hu from Wang Mang's period, when calculated with today's hu, amounts to just over nine dou, seven sheng, and four he." Therefore, it is said that the hu in the Wei Dynasty was relatively larger, and the measuring units were longer; while the hu in Wang Mang's period was relatively smaller, and the measuring units were shorter. The Liang and Chen Dynasties continued to use the ancient system of measurement. In the Qi Dynasty, five ancient sheng were counted as one dou.
In the first year of the Baoding era of the Later Zhou (561 AD), in May, the Jin state constructed granaries and discovered an ancient jade dou. By October of the fifth year of Baoding (565 AD), the emperor ordered the re-establishment of copper standards for weights and measures, ultimately achieving a state of unity and harmony. The capacity of the jade dou was measured repeatedly using millet and found to be identical to other measuring instruments. A copper sheng was then cast according to this standard and distributed for use across the nation. The inscription on the copper sheng reads: "In the first year of Baoding of the Later Zhou, in the year of Chongguang, in the month of Ruibin, when the Jin government repaired the granaries, this ancient jade dou was discovered, its shape and specifications being highly standardized, just like the excellent measuring instruments of ancient times. The Grand Master of the Jin state reported this to the emperor, and the emperor ordered it to be stored in the Tianfu. By the fifth year of Baoding, in the year of Xieqia, the emperor ordered an inspection of the measuring ropes and weights, assessing the regulations with precision, with not a hair's breadth of error nor a single grain of millet out of place. Thus, metal was melted to cast this copper sheng, which was issued nationwide, to achieve a unified system of weights and measures in a time of peace and prosperity." This is what the inscription on the jade sheng states. Now, if calculated numerically, the volume of the jade sheng is approximately 110.8 inches, while the volume of the hu is approximately 1185.739 inches. Zhen Luan also stated in "Arithmetic": "One sheng of jade equals one sheng plus three he and four spoonfuls of the official dou." Therefore, the jade sheng is relatively larger, while the official dou is comparatively smaller. Based on numerical calculations, the official dou of the Later Zhou that Zhen Luan referred to has a volume of approximately 97 inches, while the hu has a volume of approximately 977 inches. The jade dou of the Later Zhou also had accompanying gold-inlaid copper dou and a gold-inlaid copper dou from the sixth year of Jiande (577 AD), all measured using millet for capacity. Weights made of jade were used for measurement, and the weight of one sheng is six jin and thirteen liang. During the Kaihuang era, it was stipulated that the ancient three sheng equals the modern sheng. In the Daye era, the ancient system of sheng and dou was reinstated.
This discusses the ancient weighing instruments and the system of weights and measures. "Heng" means balance; "quan" means weight. The function of weighing instruments is to measure things and determine their weight. The principle behind crafting weighing instruments is akin to using a base to ensure vertical alignment and a rope to maintain straightness. If you turn left, you see the compass; if you turn right, you see the square. Weighing instruments, when viewed in a celestial context, assist in navigating the heavens; this is why it is referred to as the "jade balance." "Quan" refers to weight units such as zhu, liang, jin, jun, and shi. By using scales to weigh things, one can know their weight. In ancient times, there were also weight units like shu, zheng, chui, zi, huan, gou, zhuo, and yi, but these varied across different dynasties, and the specifics are not well-documented. The "Book of Han" states that the origin of the weighing system was determined based on the weight of the yellow bell (huangzhong). One yue holds 1,200 grains of millet, which weighs twelve zhu; twenty-four zhu equals one liang; sixteen liang equals one jin; thirty jin equals one jun; and four jun equals one shi. These five types of weighing instruments are meticulously crafted, and their manufacturing standards are determined based on principles and calibrated with physical objects. The remaining size variations are calibrated based on weight. Weighing instruments are crafted in a circular, interconnected, and continuous manner, representing an endless cycle. When weight and objects achieve balance, "heng" is established, and the operation of "heng" gives rise to the compass. The circular shape of the compass produces the square, and the square produces the rope, while the straightness of the rope produces the standard. When the standard is correct, the weighing instrument can balance, and the weighing can be accurate. These five tools are fundamental to the construction of weighing instruments and embody the essential principles guiding their design.
According to the records in the "Zhao Book," in July of the eighteenth year of Shi Le's reign, while constructing the Jiande Hall, a round stone shaped like a water mill was discovered. It was inscribed with a text: "Law and Weight Stone, weighing four jun, with consistent standards for measurements. Made by the Xin family." The "Continuation of the Discussions on Xian" dates back to the Wang Mang period. During the Jingming years of the Northern Wei, a man from Bingzhou named Wang Xianda presented an ancient bronze weighing instrument, which was inscribed with an eighty-one-character text. The inscription stated: "This is the Law and Weight Stone, weighing four jun." It also said: "The Yellow Emperor, the first ancestor, virtue extends to the Yu. The Yu Emperor, the first ancestor, virtue extends to the Xin. In the Year of the Great Beam, the dragon gathered in Wuchan. Wuchan was directly established, and heaven's mandate was bestowed upon humanity. Based on the virtue of the land, the rightful title is true. Rectifying the flawed brings longevity and prosperity. Same law for measurements, referencing the current people. The dragon is in Jisi, the year is truly Shen, initially classifying the world, all nations will eternally obey. Generations of descendants will enjoy and pass on for billions of years." This was also made during the Wang Mang period. At that time, the Grand Music Official Gongsun Chong first adjusted the weights and measures according to the "Book of Han," and after seeing this weighing instrument, he measured it with the new weights, which weighed one hundred and twenty jin. The new weights and the weighing instrument were very precisely matched. Thus, it was entrusted to Gongsun Chong for the adjustment of musical scales. During the reign of Emperor Xiaowen, the 斗 (dou) and 尺 (chi) were crafted entirely in accordance with the "Book of Han." The Liang and Chen dynasties continued to use ancient units of measurement. During the Qi dynasty, an ancient jin was eight liang. In the Zhou dynasty, the weight of one liang of jade was four and a half liang of ancient weight. During the Kaihuang era of Emperor Wen of the Sui dynasty, it was stipulated that three ancient jin equaled one jin. By the Dà Yè era of Emperor Yang of the Sui dynasty, the ancient scales were once again restored.
This talks about the conversion of weight units in different ancient dynasties, which is a bit of a mess, isn't it? In simple terms, the ancient units of 'jin' (catty) and 'liang' (tael) varied from dynasty to dynasty; sometimes they weighed more, sometimes less, which makes it really confusing. The Liang and Chen dynasties were fairly straightforward, directly using the old standards. The Qi dynasty was rather strange; their 'jin' equaled eight 'liang' from ancient times, which is quite a drop! In the Zhou dynasty, a 'liang' of jade was equivalent to four and a half 'liang' from earlier times, which is honestly kind of ridiculous! Emperor Wen of the Sui dynasty wanted to simplify things by defining three 'jin' as one 'jin,' but Emperor Yang reverted it, which is really laughable. The ancient 'jin' and 'liang' really are a puzzle!
